International Journal of Mathematics and Mathematical Sciences
Volume 30 (2002), Issue 1, Pages 31-37
doi:10.1155/S016117120200697X
An n×n matrix of linear functionals of C∗-algebras
Ajman University, P.O. Box 346, Ajman, United Arab Emirates
Received 7 March 2001
Copyright © 2002 W. T. Sulaiman. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We show that any bounded matrix of linear functionals
[fij]:Mn(A)→Mn(ℂ) has a representation
fij(a)=〈Tπ(a)xj,xi〉, a∈A, i,j=1,2,…,n, for some representation π on a Hilbert space K and an n vectors x1,x2,…,xn in K.